To solve the problem, we first need to determine how much rice is used in 8 weeks and then calculate the change in the amount of rice left in the bag.
1. **Amount of rice used every 3 weeks:**
\[
\text{Rice used per 3 weeks} = \frac{1}{4} \text{ of a 15-pound bag} = \frac{15}{4} \text{ pounds} = 3.75 \text{ pounds}
\]
2. **Number of 3-week periods in 8 weeks:**
\[
\text{Number of 3-week periods in 8 weeks} = \frac{8 \text{ weeks}}{3 \text{ weeks}} \approx 2.67 \text{ periods}
\]
However, since we must only consider complete intervals, we'll take 2 full periods.
3. **Total rice used in 6 weeks (2 complete 3-week periods):**
\[
\text{Total rice used in 6 weeks} = 2 \times 3.75 \text{ pounds} = 7.5 \text{ pounds}
\]
4. **Amount of rice used in the remaining 2 weeks:**
- Since 1/4 of the 15-pound bag takes 3 weeks, we can find out how much is used per week:
\[
\text{Rice used per week} = \frac{3.75 \text{ pounds}}{3} = 1.25 \text{ pounds}
\]
- In 2 weeks:
\[
\text{Rice used in 2 weeks} = 2 \times 1.25 \text{ pounds} = 2.5 \text{ pounds}
\]
5. **Total rice used in 8 weeks:**
\[
\text{Total rice used in 8 weeks} = \text{Rice used in 6 weeks} + \text{Rice used in 2 weeks} = 7.5 \text{ pounds} + 2.5 \text{ pounds} = 10 \text{ pounds}
\]
6. **Change in the number of pounds of rice in the bag:**
- Initial amount of rice = 15 pounds
- Amount of rice after 8 weeks = 15 pounds - 10 pounds = 5 pounds
- Change in amount of rice = Amount left - Initial amount = 5 pounds - 15 pounds = -10 pounds
Thus, the change in the number of pounds of rice in the bag after 8 weeks is:
**−10**